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Popular >

integral of 2/3 x

Solution

\int \frac{2}{3} x d x

Solution

\frac{x ^{2}}{3} + C

Solution steps

\int \frac{2}{3} x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{3} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{2}{3} \cdot \frac{x ^{2}}{2}

Simplify

\frac{2}{3} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{3}

= \frac{x ^{2}}{3}

Add a constant to the solution

= \frac{x ^{2}}{3} + C

Popular Examples

area y=3\sqrt[3]{x},0<= x<= 27 area

(\partial)/(\partial x)(sqrt(1+x^2+y^2))

\frac{\partial}{\partial x} (1 + x^{2} + y^{2})

integral from 1-2x to 1+2x of tsin(t)

\int_{1 - 2 x}^{1 + 2 x} t sin (t) d t

derivative of x/(sqrt(x^2+16))

\frac{d}{d x} (\frac{x}{x ^{2} + 16})

derivative of 7sin(3x)

\frac{d}{d x} (7 sin (3 x))

Frequently Asked Questions (FAQ)

What is the integral of 2/3 x ?
The integral of 2/3 x is (x^2)/3+C